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Electrochemical CO2 reduction has emerged as a promising CO2 utilization technology, with Gas Diffusion Electrodes becoming the predominant architecture to maximize performance. Such electrodes must maintain robust hydrophobicity to prevent flooding, while also ensuring high conductivity to minimize ohmic losses. Intrinsic material tradeoffs have led to two main architectures: carbon paper is highly conductive but floods easily; while expanded Polytetrafluoroethylene is flooding resistant but non-conductive, limiting electrode sizes to just 5 cm2. Here we demonstrate a hierarchically conductive electrode architecture which overcomes these scaling limitations by employing inter-woven microscale conductors within a hydrophobic expanded Polytetrafluoroethylene membrane. We develop a model which captures the spatial variability in voltage and product distribution on electrodes due to ohmic losses and use it to rationally design the hierarchical architecture which can be applied independent of catalyst chemistry or morphology. We demonstrate C2+ Faradaic efficiencies of ~75% and reduce cell voltage by as much as 0.9 V for electrodes as large as 50 cm2 by employing our hierarchically conductive electrode architecture. Conventional electrochemical CO2 conversion electrodes are bound by a tradeoff which prevents electrodes from being both stable and scalable. Here the authors develop a composite electrode which achieves both, enabling scaling to a 50 cm2 electrode with low ohmic losses. [ABSTRACT FROM AUTHOR]